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Question

Three solid cubes have a face diagonal of 42 cm each. Three other solid cubes have a face diagonal of 82 cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).

A
10
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B
12
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C
13
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D
15
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Solution

The correct option is B 12
Face of a cube is a square.
Diagonal of a square =2×side
So, for Cube 1:
2×side1=42
=>Side1=4cm
And for Cube 2
2×side2=82
=>Side2=8cm
So, total volume of all 6 cubes melted =3(Volume of cube_1) +3(Volume of cube_2) =3×43+3×83=1728 cu. cm.
As one large cube is formed with this volume, we have
(Side of large cube)3=1728
Side of large cube =12 cm.

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